Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8ca)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a8ca.01

Input Form

HypergeometricPFQ[{-(15/4)}, {11/2, 9/4}, z] == (1/(519775027200 z^(9/2))) ((-4 (1964655000 + 3929310000 Sqrt[z] + 1871100000 z - 1496880000 z^(3/2) - 419126400 z^2 + 2554675200 z^(5/2) - 9686476800 z^3 + 5751709425 z^(7/2) - 32070446100 z^4 - 4077627840 z^(9/2) + 17398149120 z^5 + 394974720 z^(11/2) - 1609451520 z^6 - 10076160 z^(13/2) + 40501248 z^7 + 65536 z^(15/2) - 262144 z^8 + E^(4 Sqrt[z]) (-1964655000 + 3929310000 Sqrt[z] - 1871100000 z - 1496880000 z^(3/2) + 419126400 z^2 + 2554675200 z^(5/2) + 9686476800 z^3 + 5751709425 z^(7/2) + 32070446100 z^4 - 4077627840 z^(9/2) - 17398149120 z^5 + 394974720 z^(11/2) + 1609451520 z^6 - 10076160 z^(13/2) - 40501248 z^7 + 65536 z^(15/2) + 262144 z^8)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(13/4) (29595344625 + 139272210000 z - 70741440000 z^2 + 6467788800 z^3 - 162201600 z^4 + 1048576 z^5) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(13/4) (29595344625 + 139272210000 z - 70741440000 z^2 + 6467788800 z^3 - 162201600 z^4 + 1048576 z^5) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]